Phase engineering of chirped rogue waves in Bose–Einstein condensates with a variable scattering length in an expulsive potential

We consider a cubic Gross-Pitaevskii (GP) equation governing the dynamics of Bose-Einstein condensates (BECs) with time-dependent coefficients in front term and inverted parabolic potential. Under special condition imposed on coefficients, combination phase-imprint modified lens-type transformations converts GP into integrable Kundu-Eckhaus (KE) one constant which contains quintic nonlinearity Raman-like producing self-frequency shift. The for baseband modulational instability CW states is derived, providing possibility generation chirped rogue waves (RWs) underlying matter-wave (BEC) model. Using known RW solutions KE equation, we present explicit first- second-order states. chirp RWs independent phase imprint. Detailed are presented following configurations: (i) exponentially varying time; (ii) time-periodic modulation nonlinearity; (iii) stepwise time strength expulsive Singularities local coincide valleys corresponding RWs. results demonstrate that temporal s-wave scattering length potential can be used to manipulate evolution matter BEC.